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Show y = x^4 -2 and y = kx^2 intersect all k values, how? Watch

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    Show that the curves y = x^4 - 2 and y = kx^2 intersect all values of k.
    I managed to get this so far:
    y = x^4 - kx^2 - 2 = 0

    I don't know what to do from now on though, if I use the discriminant what is the x^4 equal to like x^2 makes the a value one, what's x^4

    The actual markscheme answer can be seen here, it's 13iii
    http://www.mei.org.uk/files/papers/2011_Jan_c1.pdf

    Thank you
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    If you like, let u=x^2 and consider the quadratic u^2-ku-2=0.
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    (Original post by Magenta96)

    if I use the discriminant what is the x^4 equal to like x^2 makes the a value one, what's x^4
    Huh? Sorry, I don't understand what you're saying?

    I was going to suggest, let  A = x^2 . You now have

     A^2 - kA - 2 = 0

    You know how to solve this.
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    Try completing the square?
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    (Original post by tysonmaniac)
    Try completing the square?
    The usual method is to consider the discriminant.
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    (Original post by claret_n_blue)
    Huh? Sorry, I don't understand what you're saying?

    I was going to suggest, let  A = x^2 . You now have

     A^2 - kA - 2 = 0

    You know how to solve this.
    I meant like usually when you substitute values into the discriminant from the equation, you know how you get an A value, a B value & a C value then use those values in b^2 - 4ac, I don't get what I'd use for that A value. I'd get stuck at k^2 - (4 x (a term) x -2) > 0, I don't understand what that term would be
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    (Original post by BabyMaths)
    If you like, let u=x^2 and consider the quadratic u^2-ku-2=0.
    hi, thanks for answering, where has the u - x^2 come from? Did you divide the x^4 by 2, because then how come you don't divide the -2 at the end by 2 as well if the whole equation is divided by 2?
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    (Original post by Magenta96)
    hi, thanks for answering, where has the u - k^2 come from?
    You are looking at is a disguised quadratic

    Are you saying that you do not know what the discriminant is for

    u^2 - ku - 2 = 0
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    (Original post by Magenta96)
    I meant like usually when you substitute values into the discriminant from the equation, you know how you get an A value, a B value & a C value then use those values in b^2 - 4ac, I don't get what I'd use for that A value. I'd get stuck at k^2 - (4 x (a term) x -2) > 0, I don't understand what that term would be
    Oh ok. Well look at the new quadratic I have given you. You can work out the 'a' value from here can't you? The equation is the same as the one BabyMaths gave you, the only difference is that in that equation, you used the substitution  u = x^2 instead of  A = x^2.
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    The A value is always the highest power of the X, the B the second lowest and C the lowest
    So A would be 1 as it's the coefficient for the highest X power (x^4)
    B would be -k as it's the second lowest power of X (x^2)
    And C would be -2 as it's the lowest power of X (x^0)
    Hope this helps however for the answer to the question I can't help you lmao im stuck
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    This is a 4 year old thread. Closed.
 
 
 
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